Educational Research (ISSN: 2141-5161) Vol. 2(2) pp. 864-873 February 2011
Available online@ http://www.interesjournals.org/ER
Copyright ©2011 International Research Journals
Full Length Research Paper
A predictive model for mathematical performance of
blind and seeing students
Pezeshki Poorya1, Alamolhodaei Hassan2, Radmehr Farzad2
1
Faculty of Mathematical Science, Islamic Azad University Science and Research Branch, Tehran, Iran
2
Faculty of Mathematical Science, Ferdowsi University of Mashhad, Mashhad, Iran
Accepted 09 February, 2011
The main objective of this study was to explore the relationship among working memory, mathematics
anxiety, mathematics attitude and math performance in order to examine their effects on seeing and
blind students. A sample of 97, middle school blind and seeing students were assessed on (a) Digit
Span Backwards Test (DBT) (b) Mathematics Anxiety Rating Scale (MARS) (c) Math attitude test and (d)
Math exam. The Results indicated that seeing students showed more achievement in math
performance, and much more positive attitude toward math than blind students. But there was no
significant difference between blind and seeing student in working memory capacity and math anxiety.
These findings could help provide some practical implications for improving blind students’ math
performance and studying their math disabilities.
Keywords: Mathematical Performance, Working Memory Capacity, Math Anxiety, Math Attitude, Blind
Students
INTRODUCTION
Mathematics is a universal subject and as a part of our
life, anyone who is a participating member of society
should know basic concept of mathematics. Students’
mathematical achievement, however, is ultimately
determined and limited by the opportunities they have
had to learn. Mathematics is not restricted to a selected
group of students (Moenikia and Zahed-Babelan, 2010)
“All students must learn to think mathematically, and
they must think mathematically to learn” (Kilpatrick et al.,
2001). In this study, the effect of following factors on the
math performance of blind and seeing students was
studied: working memory capacity (WMC), mathematics
anxiety and mathematics attitude. To this end, a model
was developed and the contribution of each of these
psychological factors to mathematical performance of the
group in question was included.
Working memory
Working memory is one of the main concepts of cognitive
*Corresponding author Email: pooryapezeshki@gmail.com
psychology that has played a growing role over the past
decades in accounting for cognitive processes (Baddeley,
1990; Baddeley and Hitch, 1974).
Short-term memory was originally construed as a
somewhat buffer of seven plus or minus two storage units
(Miller, 1956). Researchers also demonstrated the need
for a more dynamic conceptualization of short-term
memory, that Baddeley called it working memory
(Baddeley and Hitch, 1974; Baddeley, 1986, 1998).
Baddeley and Hitch (1974) advocated that temporary
memory processes, despite of involving dedicated
memory systems, should be viewed within the context of
more general cognitive mechanisms. For many
researchers this calls toward a more functional view of
memory, matched by the adoption of the term ‘working
memory,’ that marks the start of a modern era of
research into the characteristics of memory and its role in
a range of mental activities. Remarkably, working
memory has almost become a universal phrase among
researchers in cognition and indeed in neuroscience.
The working memory (WM) has a limited capacity
system being responsible for the manipulation and
storage of information during the performance of
cognitive tasks such as comprehension learning, problem
solving, and reasoning (Baddeley, 1986). The multi-
Pezeshki et al 865
component model of WM proposed by Baddeley and
Hitch (1974), is arguably the most widely cited model
which comprises four sub-components. The phonological
loop (Baddeley, 1986) and the visuo-spatial sketchpad
(Logie, 1995) are two sub-components which are
assumed to be responsible for storing and manipulating
verbal or visuospatial information. They are co-ordinated
by a domain-general limited capacity system, the control
executive (the third sub-component), which commands
some of functions including planning, inhibition, switching
attention, and monitoring the processing of temporarily
held information (Baddeley, 1986, 1996; Baddeley and
Logie, 1999). The forth added part, the episodic buffer
(Baddeley, 2000), is considered to be responsible for the
integration of information from the subcomponents of WM
and long term memory (LTM).
More definitions of working memory have been
suggested:
The functional definition of working memory results
from the assumption declared that WM is involved in
many real-world activities (e.g. Baddeley and Hitch,
1974). In other words, working memory is a necessary
construct because a great amount of daily activities
involve activity holding in mind, manipulating, and
integrating information in memory. For example,
mathematical problems often involve remembering the
totals of certain calculations while performing other
mathematical operations and then combining the
outcomes.
Working memory refers to the ability to hold information
in mind while manipulating, and integrating other
information in the service of some cognitive goal (Kane
and Engle, 2002; Roberts and Pennington, 1996).
Working memory capacity is widely measured by using
complex memory paradigms, in which participants are
required to combine memory for sequences of items
whose presentation is interleaved by processing
activities. The number of items to be remembered is
increased until the maximum length at which memory
accuracy is maintained.
According to the working memory model advanced
originally by Baddeley and Hitch (1974) and developed
subsequently by Baddeley and colleagues (Baddeley,
1996, 2000; Baddeley and Logie, 1999), working memory
reflects multiple resources associated with distinct
capacity-limited sub-systems. This model incorporates
the central executive, which is associated with attentional
control, high-level processing activities and coordination
of activities within working memory.
An important role has been ascribed to workingmemory capacity in reading comprehension, little
consensus
exists
in
its
conceptualization,
operationalization, measurement, and assessment
(Friedman and Miyake, 2004; Juffs, 2004; Koda, 2005;
MacDonald and Christiansen, 2002; Traxler, 2006;
Waters and Caplan, 1996).
There are some considerable evidences suggesting
that WM may be important for mathematics learning and
problem solving. For example, Adams and Hitch (1998)
suggested that mental arithmetic performance relies on
the recourses of working memory. Significant
associations have been found between the phonological
loop and mental arithmetic performance in children
(Adams and Hitch, 1997, 1998; Javris and Gathercole,
2003; Holmes and Adams, 2006). More specifically,
Holmes and Adams, (2006) reported a significant
association between children's WM ability and their
mathematics attainment. They found that WM could
predict national curriculum-based mathematical skills. In
addition, the result of their study confirmed pervious
findings that the central executive is an important
predictor of children’s mathematical performance. The
phonological loop showed a stronger association with the
older children’s mental arithmetic performance.
Moreover, Alamolhodaei (2009) and also others (Ekbia,
2000) have found that the students with high WMC
(hWMC), regardless the gender, are more capable of
solving math word problems compared to those with low
WMC (LWMC). Individuals differ in their working memory
space; Any overload leaves students with no space for
thought and conceptual organization, so faulty learning
takes place (Johnstone and El-Banna 1989; Johnstone
1984; Johnstone and Al-Naeme 1991; Johnstone et al.
1993; Harel and Kaput 1991; Cowan 2005).
Mathematics Attitude
Attitude is an important concept for learning mathematics
also it is a mental set or disposition of readiness to
respond and the psychological basis of attitudes,
permanence, learned nature and character evaluative. It
includes peoples, places, ideas or situations. Attitudes
are not just a passive result of past experience; instead
they impel behavior and guide its form and manner. The
components of attitudes are: (i) a cognitive component
(opinion information or strength of belief or disbelief; (ii).
an affective component (emotional component of like (or)
dislike) and (iii) an action (co nature behavioral
component of habit or readiness to respond)
(Guimaraest, 2005).
The attitudes of students towards lesson effects on
their success, interests and job selection (Koc and Sen,
2006). Especially some students have quite negative
opinions about math because of negative behaviors of
teachers or wrong experiences. These students have
some prejudice such as mathematics is a complicated
lesson and only those who have math intelligence can
learn it. This situation is continuies during the school
years and students’ self-confidence disappears as a
result. Changing the negative attitudes of students into
positive can be provided if the teachers increase the
866 Educ. Res.
positive experiences of students towards Math. The
Fennema-Sherman Mathematics Attitude Scales were
developed in 1976 and it has become one of the most
popular instruments used in research over the last three
decades. The Fennema-Sherman Mathematics Attitude
Scales consist of a group of nine instruments: (1) Attitude
Toward Success in Mathematics Scale (2) Mathematics
as a Male Domain Scale (3) and (4) Mother/Father Scale
(5) Teacher Scale (6) Confidence in Learning
Mathematics Scale (7) Mathematics Anxiety Scale (8)
Effectance Motivation Scale in Mathematics, and (9)
Mathematics Usefulness Scale.
Mathematics attitude should be viewed as a
predisposition to respond in an unfavorable or favorable
way to mathematics. By accepting this view, mathematics
attitude includes relevant beliefs, behaviors and
attitudinal or emotional reactions. Researches indicated
that, there is a positive relation between mathematics
attitude and mathematics achievement (Ma and Kishor,
1997a; Saha, 2007; Thomas, 2006).
Researchers have revealed that some variables
mediating the effect of math attitude and mathematics
achievement (Kabiri and Kiamanesh, 2004; Kiamanesh et
al., 2004). Some of these variables are intelligence
quotient (Blair et al., 2005; Bull and Scerif, 2001; Evans
et al., 2002; Grissmer, 2000) and motivation for
mathematics (Khoush et al., 2005; Yunus and Ali, 2009).
Many students taking math courses have a negative
attitude toward math that can be described as math
anxiety or feeling of tension or fear interferes with math
performance.
Mathematics anxiety
Mathematics anxiety is one of the common attitudinal and
emotional factors that has attached attention in recent
years. Over the past thirty years, studies have shown
mathematics anxiety is a highly prevalent problem for
students (Baloglu and Koçak, 2006; Betz, 1978; Jain and
Dowson, 2009; Ma and Xu, 2004; Rodarte-Luna and
Sherry, 2008, Alamolhodaei, 2009). Although there is no
general consensus about mathematics anxiety among
researchers regarding its definition, dimensions, causes
and effects. It has been directly or indirectly, affecting all
aspects of mathematics education as one of the most
commonly investigated constructs in mathematics
education (Çatlıoğlu et al., 2009).
A great number of definitions has been suggested for
mathematics anxiety. Some are as follows:
Mathematics anxiety is first introduced as ‘‘the presence
of a syndrome of emotional reactions to arithmetic and
mathematics’’ (Dreger and Aiken, 1957, p. 344).
Mathematics anxiety is defined as a feeling of tension,
apprehension, or fear that interferes with math
performance (Richardson and Suinn, 1972).
According to Tobias and Weissbrod, mathematics
anxiety is the panic, feeling of unassistedness,
paralization and mental disorders when students wish to
solve an arithmetical problem (1980).
Mathematics anxiety is a situation which shows itself
with emotional stress and anxiety when the individual is
faced with cases such as solving arithmetical problems or
doing operations with numbers in either his school or
everyday life. This anxiety state can cause amnesia and
loss of self confidence (Tobias, 1993).
Math anxiety usually arises when students are faced
with unknown or ambiguity and find it frightening rather
than enjoyable challenging. Math anxiety is not an
isolated phenomenon as it originates and persists within
a complex learning process with serious
long-term effects (Bessant, 1995).
A number of studies had been done over the last
decades on mathematic anxiety; some of these are
presented below:
According to the results of a meta-analysis including
151 studies, Hembree (1990) found that mathematics
anxiety is related to poor performance on mathematics.
He also found significant differences in mathematics
anxiety levels across ability, grade level, and fields of
study
Chipman and others (1992) reported that mathematics
anxiety is negatively correlated with students’ interests in
a scientific career regardless of their level of
mathematical skills or gender.
Ashcraft and colleagues (Ashcraft and Faust, 1994;
Faust et al., 1996) found that math anxiety had little effect
on simple addition and multiplication problems. The
solving of more complex arithmetic problems (e.g.,
arithmetic with carrying), however, was affected by MA.
The most dominant theory of MA, posited by Ashcraft and
colleagues, claims that MA individuals have difficulty with
complex mathematical problem solving because MA
induced ruminations occupy their working memory (WM;
see Ashcraft, 2002).
The symptoms of math anxiety can be diverse,
including nausea and stomachache, a ‘blank’ mind,
extreme nervousness, inability to hear the teacher and/or
noise sensitivity, inability to concentrate, and negative
self-talk (Kitchens, 1995).
Individuals’ high mathematics anxiety have been shown
to perform worse than their low-mathematics anxious
peers in solving difficult mathematical problems (Ashcraft
and Kirk, 2001; Ashcraf et al., 1998; Ashcraft et al., 2007,
Alamolhodaei and Farsad, 2009).
Students accustomed to solving problems without time
restrictions might develop anxiety if told they need to
solve problems quickly (Ashcraft and Moore, 2009).
The goal of the current study was to determine the role
of math performance, math anxiety, math attitude and
working memory space in blind and seeing students.
The first objective of the study was to discover whether
Pezeshki et al 867
there would be relationship between students WMC and
math performance.
The second objective of this research was to discover
whether there would be a relationship between math
performance and blind or seeing students.
The third objective was to compare working memory
capacity of blind and seeing student.
The fourth objective was to compare math anxiety of
blind and seeing student
The fifth objective was to compare math attitude of
blind and seeing student and the last objective was
compare math anxiety of genders.
MATERIALS AND METHODS
Cronbach’s alpha, the degree of internal consistency of (MARS)
items for this study, was estimated to be 0.87. The score ranged
from 23 to 83 with the mean of 55.44. The sample was divided into
high/medium/low MA groups based upon the previous study (Clute,
1984; Alamolhodaei, 2009).
Math Attitude Test
Level of attitude was determined by math unpublished attitude test
which has been used in Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad. It consists of 18 items about
attitude toward math based on Fennema-Sherman Mathematics
Attitude Scales. The students were assigned the degree of math
attitude aroused using a three rating scale ranging from high to low
(3–l). Cronbach’s alpha, the degree of internal consistency of
attitude items for this study, was estimated to be 0.77. The sample
was divided into high/medium/low math attitude groups.
Participants
58 middle school seeing students including 24 girls and 34 boys
and 39 middle school blind students including 21 girls and 18 boys
were selected from schools of Khorasan Razavi Province using
random multistage stratified sampling design.
Procedures
The participants were required to take the following tests:
1- Digit Span Backwards Test (DBT)
2- Mathematics Anxiety Rating Scale (MARS)
3- Math Attitude Test
4-Math Exam
Digit Span Backwards Test (DBT)
For the measurement of the students’ working memory capacity
(WMC), DBT has been quoted as the normal test (Case 1974;
Scardamalia 1977; Al-Naeme 1989, Niaz 1988; Talbi 1990;
Johnstone et al. 1993, Alamolhodaei, 2009). The digits were read
out by an expert and the students were asked to listen carefully,
then turn the number over in their mind and write it down from left to
right on their answer sheets. Students were tested by DBT two
times within 2 months as a test and retest.WMC was originally has
seven plus or minus two storage unit as pascual leoni described. In
this study, the students who scored less or equal to four were
labeled as low WMC, those group who scored more than 4 and less
than 5 were labeled as intermediate WMC group and those who
scored more than 5 were labeled as high WMC group.
Mathematics Anxiety Rating Scale (MARS)
Level of anxiety was determined by the score attained on the Math
Anxiety Rating Scale (MARS), which has been used recently in the
Faculty of Mathematical Sciences, Ferdowsi University of Mashhad.
The MARS for this research was newly designed by the
researchers of this study according to the inventory test of
Ferguson (1986). It consists of 19 items, each of which item
presents an anxiety arousing situation. The students were assigned
degree of anxiety and abstraction anxiety aroused using a five
rating scale ranging from very much to not at all (5–l). The five
items were hypothesized to measure a new component of math
anxiety being distinctive from those already identified by others
(Suinn 1970; Richardson and Suinn 1972). These items were used
to identify abstraction anxiety, according to Ferguson (1986).
Math Exams
The effectiveness of these tests was evaluated by determinig the
students’ performance in mathematical problem solving. Math exam
was consisted of 20 questions base on middle school math syllabi.
Here is a typical question of math exam of this study:
For producing one kind of bread we should combine material A and
B with the ratio 2 and 5.
For producing 42 grams of this bread, how much gram from
material A and B would be needed?
RESULTS
Comparing math performance and Working Memory
Capacity
The result of one-way ANOVA for three groups of
working memory capacity showed that all were
significantly different in terms of mean scores obtained in
Math exam with p-value less than 0.001 (Table 1).
Graph error bar has shown significant difference among
math learners performance according to working memory
capacity (Figure 1)
The circle in the graph represent the mean of the
shows upper and
response variable and each of
lower boundaries with a 95 percent confidence interval
which means that the mean of variable with 95 percent
probability is in the range that the graph denoted and also
we should say that two or more mean’s groups haven’t
significant difference if there is a horizontal line that
intersects corresponding vertical lines.
As can be seen in this graph, Students with low WMC
had less achievement in math performance than medium
WMC. Also they had less achievement in math
performance than high WMC. Students with medium
WMC had less achievement in math performance than
these in high WMC group.
868 Educ. Res.
Table1. Comparing math performance and WMC
Between Groups
Within Groups
Total
Sum of Squares
121.688
480.440
602.128
Df
2
94
96
Mean Square
60.844
5.111
F
11.904
Sig.
.000
Figure 1. Graph comparing math performance and WMC
Table 2. Comparing math anxiety and gender
Comparing math anxiety and gender
The result of t-test for two groups of male and female
students showed that they had significant difference in
terms of mean scores obtained in Mathematics Anxiety
Rating Scale with p-value 0.030 additionally it was shown
that female students had more mathematics anxiety than
male ones (Table 2).
Comparing math performance of blind and seeing
students
The result of t-test for two groups of blind and seeing
student showed that they had significant difference in
terms of mean scores obtained in Mathematic
performance with p-value less than 0.001. It was found
that seeing students had more achievement in math
Pezeshki et al 869
Table 3. Comparing math performance of blind and seeing students
Figure 2. Graph comparing math performance of blind and seeing students
Table 4. Comparing math attitude in blind and seeing students
performance than blind students. Graph error bar showed
this difference much better (Table 3 and figure 2).
Comparing
students
math
attitude in
blind
and
seeing
The result of t-test for two groups of blind and seeing
students showed that they had significant difference
in terms of mean scores obtained in Mathematics attitude
exam with p-value 0.049 also seeing students were found
to have much positive attitude toward math than blind
students (Table 4).
870 Educ. Res.
Table 5. Comparing working memory in blind and seeing students
Figure 3. Graph Comparing working memory in blind and seeing students
Comparing working memory in blind and seeing
students
The result of t-test for two groups of blind and seeing
students showed that they hadn’t significant difference
in terms of mean scores obtained in Digit Span
Backwards Test with p-value 0.096 although graph error
bars shown that in this study seeing students had more
WMC than blind students (Table 5 and Figure 3).
Comparing math anxiety in blind or seeing students
The result of t-test for two groups of blind and seeing
students showed that they had not significant difference
in terms of mean scores obtained in Mathematics Anxiety
Rating Scale with p-value 0.598, although graph error
bars showed that in this study blind students had more
math anxiety than seeing students (Table 6 and Figure 4)
.
DISCUSSION
As mentioned earlier, in this research, the authors
studied the effect of Working memory capacity,
mathematics anxiety and mathematics attitude on math
performance of blind and seeing students. The main aim
of this study was to study the different size of effect of
these factors among blind and seeing students.
Many researchers reported that, there is significant
difference between high WMC students and low WMC
Pezeshki et al 871
Table 6. Comparing math anxiety in blind or seeing students
Figure 4. Graph comparing math anxiety in blind or seeing students
ones in math performance (Adam and Hitch 1998; Ekbia,
2000; Alamolhodaei, 2009). Also in the sample of this
study that included both blind and seeing students,
different math performance (between students with high
WMC and low WMC) was seen (P-value less than .001).
In some of previous studies, math anxiety between
male and female students was studied. The results
indicated that females display more math anxiety than
males( Alamolhodaei, 2009; Woodard, 2004). In the
present study same results were obtained and confirming
females show more math anxiety than males.
When dealing with math problems, Blind students face
many difficulties for example they do not know how to get
the information of problems, cannot draw the schemata of
math problems and cannot provide the instrument for
solving math problems. Also the lack of guiding math
book for blind student is another problem that they have.
These problems are possible causes for the
differences shown in this study. It was found that seeing
students had better performance than blind students ( Pvalue less than .001) and this deference is very much
according to graph error bars.
The inferior achievement that blind students showed in
math performance and the problems that they have in
problem solving caused math attitude of blind students to
be more negative than seeing students (P-value .049).
Another important finding of this study was that, there
was no significant difference between WMC of blind and
seeing students. Accordingly, it would be valuable to
reconsider educational method and mathematical
872 Educ. Res.
curriculum for blind students. In other words, based upon
WMC blind and seeing learners may have roughly the
same performance in mathematical problem solving.
As it was found in this study, no significant difference
was found between math anxiety of blind and seeing
students, despite the higher mean of blinds. After
interviewing blind learners, authors found that a lot of
failure in the previous math exams and their inferior
achievement caused them to feel that the achievement of
good math result would not so important for them.
Therefore, this belief and lack of anxious about math
exams caused them to be far from rigid math anxiety
Considering these results, as a math teacher, we
should pay attention to how learners think and learn,
therefore making the necessary opportunity for all
learners, in particular, blind ones. Blind students should
be encouraged to change their views about math lessons
so they can perform on math problem solving the same
as ordinary students, if they want.
It would be valuable to continue this study in other
areas and with more Blind students to find how well the
model of this research would work.
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